Mountain railway alignment optimization using stepwise & hybrid particle swarm optimization incorporating genetic operators

Optimizing railway alignments is a quite complex and time-consuming engineering problem. The huge continuous search space, complex constraints, implicit objective function and infinite potential alternatives of this problem pose many challenges. Especially in mountainous regions, finding a near-optimal alignment for extremely complex terrain and constraints is a most arduous task, which cannot be solved satisfactorily with most existing methods. In this study, a stepwise & hybrid particle swarm-genetic algorithm is developed for railway alignment optimization in mountainous regions. It is a continuous search method suitable for railway alignment design. A stepwise horizontal–vertical–integral approach which defines the horizontal and vertical alignments as two kinds of particles, is proposed to solve the three-dimensional railway alignment optimization problem. To enhance the initial diversity and momentum, butterfly-shaped areas are preset on a path generated with a bidirectional distance transform for initializing horizontal particles. For the solution method, specific genetic operators, including roulette wheel selection, four crossovers and two mutations are integrated into the stepwise particle swarm method to address parameter-dependent performance and avoid premature convergence. In addition, a cubic polynomial weight update strategy is employed for thoroughly searching the problem space. This synthesis method has been applied to a real-world case in a very mountainous region. The detailed data analyses demonstrate that it can offer more promising solutions compared with alternatives designed by experienced designers and those generated with a genetic algorithm or non-stepwise particle swarm algorithm.